When you move your sats to fund onchain lightning node here you already gave up your privacy unless you opened onchain lightning opening using postmix tools. So that’s #1 step that is most important because some entity knows that this utxo that belongs to you was used to open that LN channel. Also muun is not a lightning wallet it’s actually an onchain wallet with an onchain to lightning swap service. It’s not a true LN wallet, even when you receive LN onchain fees are paid. Also muun charges a fee for failed payment attempts and they simply approximate by paying you LN with a swap onchain balance into LN and they pay an invoice for you. Also using this tool

Lightning Decoder

Decode Lightning Network Requests - BOLT11, LNURL, and Lightning Address

Lightning Decoder is a tool for decoding Lightning Network request codes - BOLT11s, LNURL codes, and Lightning Addresses are supported.

Your LN tx are not private

I think lightning tx are private if I do not have a direct channel between payer and receiver. Lightningdecoder.com does not discover any identifyable information.